OPCL coupling of mixed integer-fractional order oscillators: tree and chain implementation

Abstract

Controlling coupled oscillators and their application are important in diverse areas of nonlinear science and technology. In this paper, a unidirectional Open-Plus-Closed-Loop coupling (OPCL) scheme in controlling two mixed oscillators with emphasis on fractance and integer-order configurations was introduced. The appropriate choice of the controller between coupled non-identical oscillators is justified to achieve the coexistence of anti-phase and complete synchronization via amplitude death. The possibility of controlling one response variable, keeping the other pairs of variable undisturbed are deduced with different configurations. This type of mixed synchronization emanated from coupled integer and fractional-order Sprott-A oscillators without interception and loss of stability. The main novelty in this work is the analog implementation for the coupled integer-order, tree, and chain configurations which are simulated and discussed extensively.